Critical fluctuations of noisy period-doubling maps

Andrew E. Noble (), Saba Karimeddiny, Alan Hastings and Jonathan Machta
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Andrew E. Noble: University of California
Saba Karimeddiny: University of Massachusetts
Alan Hastings: University of California
Jonathan Machta: University of California

The European Physical Journal B: Condensed Matter and Complex Systems, 2017, vol. 90, issue 1, 1-6

Abstract: Abstract We extend the theory of quasipotentials in dynamical systems by calculating, within a broad class of period-doubling maps, an exact potential for the critical fluctuations of pitchfork bifurcations in the weak noise limit. These far-from-equilibrium fluctuations are described by finite-size mean field theory, placing their static properties in the same universality class as the Ising model on a complete graph. We demonstrate that the effective system size of noisy period-doubling bifurcations exhibits universal scaling behavior along period-doubling routes to chaos.

Keywords: Statistical; and; Nonlinear; Physics (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1140/epjb/e2016-70641-1

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